[tex]\(\begin{matrix}
y=ln(x+3)\\
e^y=x+3\\
e^y-3=x\\
swap ~x~and~y\\
\huge\underline{y=e^x-3}}
\end{matrix}\)
[/tex]
To get the inverse
of any function f(x) [ just make sure that it passes the horizontal line test]
follow the steps:
- Solve for x, i.e separate x in one side
and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original
function [tex]f^{-1}(x)[/tex].
-------------------------
Apply that on your function
[tex]\(\begin{matrix}
y=ln(x+3)\\
e^y=x+3\\
e^y-3=x\\
swap ~x~and~y\\
\huge\underline{y=e^x-3}}
\end{matrix}\)
[/tex]
